Quantum simulation of the spin-boson model: monitoring the bath

The spin-boson model occupies a central position in condensed matter physics. It describes the interaction between a two-level system and a collection of harmonic oscillators or dissipative bath. It was originally developed as a general, fully quantum-mechanical, framework to account for the dissipation inherent to any quantum system [1]. This formalism was successfully applied to various physical systems weakly coupled to a bosonic bath (mesoscopic circuits, amorphous solids\textellipsis ). However only a few experiments [2,3] explored its more challenging limit -when the quantum system is strongly coupled to the many degrees of freedom of the bath - despite numerous theoretical predictions. In this regime the ground state of the whole system is non-trivial: the spin is highly entangled with the bath, forming a many-body system. I will present a new architecture based on superconducting circuits to tackle this challenging problem. It offers two main advantages: first it allows to reach the ultra-strong coupling between the quantum system and its bath; second one can experimentally monitor the qubit and its bath at the same time, and thus reveal the many-body correlations which are building up when all the degrees of freedom become entangled. Our approach consists in coupling a superconducting artificial atom (namely a transmon qubit) to a meta-material made of thousands of SQUIDs. The latter sustains many photonic modes and shows characteristic impedance close to the quantum of resistance. As a direct application, we use this circuit to explore quantum optics in the ultrastrong coupling regime, where new phenomena arise [4--7]. [1] Leggett, A. et al., Rev. Mod. Phys. 59(1), 1 (1987). [2] Forn-D\'{\i}az, P. et al., Nat. Phys. AOP (2016). [3] Haeberlein, M. et al., arXiv: 1506.09114 (2015). [4] Le Hur K., Phys. Rev. B 85, 140506(R) (2012). [5] Goldstein M. et al., Phys. Rev. Lett. 110, 017002 (2013). [6] Gheeraert N. et al., arXiv :1601.01545 (2015). [7] Yoshihara F. et al., Nat. Phys. AOP (2016).